{"id":"https://openalex.org/W2055024656","doi":"https://doi.org/10.1007/s002000050059","title":"Linear Bijections and the Fast Fourier Transform","display_name":"Linear Bijections and the Fast Fourier Transform","publication_year":1997,"publication_date":"1997-01-27","ids":{"openalex":"https://openalex.org/W2055024656","doi":"https://doi.org/10.1007/s002000050059","mag":"2055024656"},"language":"en","primary_location":{"id":"doi:10.1007/s002000050059","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s002000050059","pdf_url":null,"source":{"id":"https://openalex.org/S44535979","display_name":"Applicable Algebra in Engineering Communication and Computing","issn_l":"0938-1279","issn":["0938-1279","1432-0622"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applicable Algebra in Engineering, Communication and Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5009262102","display_name":"Markus Hegland","orcid":"https://orcid.org/0000-0002-5136-2883"},"institutions":[{"id":"https://openalex.org/I118347636","display_name":"Australian National University","ror":"https://ror.org/019wvm592","country_code":"AU","type":"education","lineage":["https://openalex.org/I118347636"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"M. Hegland","raw_affiliation_strings":["Centre for Mathematics and its Applications, School of Mathematical Sciences, Australian National University, Canberra ACT 0200, Australia, , , , , , AU","Centre for Mathematics and its Applications, School of Mathematical Sciences, Australian National University, Canberra ACT 0200, Australia, , AU"],"affiliations":[{"raw_affiliation_string":"Centre for Mathematics and its Applications, School of Mathematical Sciences, Australian National University, Canberra ACT 0200, Australia, , , , , , AU","institution_ids":["https://openalex.org/I118347636"]},{"raw_affiliation_string":"Centre for Mathematics and its Applications, School of Mathematical Sciences, Australian National University, Canberra ACT 0200, Australia, , AU","institution_ids":["https://openalex.org/I118347636"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5034630461","display_name":"Wayne W. Wheeler","orcid":null},"institutions":[{"id":"https://openalex.org/I118347636","display_name":"Australian National University","ror":"https://ror.org/019wvm592","country_code":"AU","type":"education","lineage":["https://openalex.org/I118347636"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"W. W. Wheeler","raw_affiliation_strings":["Centre for Mathematics and its Applications, School of Mathematical Sciences, Australian National University, Canberra ACT 0200, Australia, , , , , , AU","Centre for Mathematics and its Applications, School of Mathematical Sciences, Australian National University, Canberra ACT 0200, Australia, , AU"],"affiliations":[{"raw_affiliation_string":"Centre for Mathematics and its Applications, School of Mathematical Sciences, Australian National University, Canberra ACT 0200, Australia, , , , , , AU","institution_ids":["https://openalex.org/I118347636"]},{"raw_affiliation_string":"Centre for Mathematics and its Applications, School of Mathematical Sciences, Australian National University, Canberra ACT 0200, Australia, , AU","institution_ids":["https://openalex.org/I118347636"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5009262102"],"corresponding_institution_ids":["https://openalex.org/I118347636"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":0.4265,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.66899909,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"8","issue":"2","first_page":"143","last_page":"163"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11034","display_name":"Digital Filter Design and Implementation","score":0.9944000244140625,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11034","display_name":"Digital Filter Design and Implementation","score":0.9944000244140625,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9876999855041504,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.9807000160217285,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/bijection-injection-and-surjection","display_name":"Bijection, injection and surjection","score":0.9430817365646362},{"id":"https://openalex.org/keywords/fast-fourier-transform","display_name":"Fast Fourier transform","score":0.7663015127182007},{"id":"https://openalex.org/keywords/prime-factor-fft-algorithm","display_name":"Prime-factor FFT algorithm","score":0.7550250291824341},{"id":"https://openalex.org/keywords/bijection","display_name":"Bijection","score":0.7378041744232178},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7223166227340698},{"id":"https://openalex.org/keywords/split-radix-fft-algorithm","display_name":"Split-radix FFT algorithm","score":0.6357994079589844},{"id":"https://openalex.org/keywords/congruence-relation","display_name":"Congruence relation","score":0.5371350646018982},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.4833190441131592},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4740060269832611},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.473020076751709},{"id":"https://openalex.org/keywords/equivalence-relation","display_name":"Equivalence relation","score":0.44562849402427673},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3561820089817047},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3284305930137634},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.3091402053833008},{"id":"https://openalex.org/keywords/fourier-analysis","display_name":"Fourier analysis","score":0.22921746969223022},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08706647157669067},{"id":"https://openalex.org/keywords/fractional-fourier-transform","display_name":"Fractional Fourier transform","score":0.06264945864677429}],"concepts":[{"id":"https://openalex.org/C48659774","wikidata":"https://www.wikidata.org/wiki/Q4907197","display_name":"Bijection, injection and surjection","level":3,"score":0.9430817365646362},{"id":"https://openalex.org/C75172450","wikidata":"https://www.wikidata.org/wiki/Q623950","display_name":"Fast Fourier transform","level":2,"score":0.7663015127182007},{"id":"https://openalex.org/C77928272","wikidata":"https://www.wikidata.org/wiki/Q7243214","display_name":"Prime-factor FFT algorithm","level":5,"score":0.7550250291824341},{"id":"https://openalex.org/C24424167","wikidata":"https://www.wikidata.org/wiki/Q180907","display_name":"Bijection","level":2,"score":0.7378041744232178},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7223166227340698},{"id":"https://openalex.org/C103755468","wikidata":"https://www.wikidata.org/wiki/Q17103599","display_name":"Split-radix FFT algorithm","level":5,"score":0.6357994079589844},{"id":"https://openalex.org/C9973445","wikidata":"https://www.wikidata.org/wiki/Q8349849","display_name":"Congruence relation","level":2,"score":0.5371350646018982},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.4833190441131592},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4740060269832611},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.473020076751709},{"id":"https://openalex.org/C156103551","wikidata":"https://www.wikidata.org/wiki/Q130998","display_name":"Equivalence relation","level":2,"score":0.44562849402427673},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3561820089817047},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3284305930137634},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.3091402053833008},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.22921746969223022},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08706647157669067},{"id":"https://openalex.org/C76563020","wikidata":"https://www.wikidata.org/wiki/Q4817582","display_name":"Fractional Fourier transform","level":4,"score":0.06264945864677429}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s002000050059","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s002000050059","pdf_url":null,"source":{"id":"https://openalex.org/S44535979","display_name":"Applicable Algebra in Engineering Communication and Computing","issn_l":"0938-1279","issn":["0938-1279","1432-0622"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applicable Algebra in Engineering, Communication and Computing","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.50.1194","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.50.1194","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ftp://nimbus.anu.edu.au/pub/Hegland/hegw94.ps.gz","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W1964153492","https://openalex.org/W1971407031","https://openalex.org/W2019203901","https://openalex.org/W2037026538","https://openalex.org/W2040077566","https://openalex.org/W2061171222","https://openalex.org/W2068803999","https://openalex.org/W2134572726","https://openalex.org/W2162611351"],"related_works":["https://openalex.org/W2031343199","https://openalex.org/W2200032781","https://openalex.org/W4362564158","https://openalex.org/W2977460836","https://openalex.org/W2356814585","https://openalex.org/W2144412928","https://openalex.org/W4246835537","https://openalex.org/W2113951268","https://openalex.org/W2012363129","https://openalex.org/W2055024656"],"abstract_inverted_index":null,"counts_by_year":[{"year":2019,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
